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# Math ch.7 vocab

Pythagorean triple a set of three positive integers, b, and c that satisfy the equation c2=a3+b2.
trigonometric ratio a ratio of the lengths of two sides in a right triangle
tangent the ratio is called that the tangent
sine a trigonometric ratio for acute angles that involve the lengths of a leg and the hypotenuse of a right triangle
cosine a trigonometric ratio for acute angles that involve the lengths of a leg and the hypotenuse of a right triangle
angle of elevation of you look up at an object, the angle your line of sight makes with a horizontal line.
angles of depression of you look down at an object, the angles your line of sight makes with a horizontal line.
solve a right triangle this means to find the measures of all its sides and angles.
inverse tangent using the opposite and adjacent sides from the angle to find the degrees of the angle
inverse sine using the adjacent and hypotenuse of a triangle to find the degrees of the angle.
inverse cosine using the opposite and the hypotenuse of the triangle to figure out the degrees of the angle.
theorems
Pythagorean Theorem in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
Converse of the Pythagorean Theorem If the square of the length of the longest side of a triangle is equal to the sum of the squares of the lengths of the other two sides then the triangles is a right triangle
Converse of the Pythagorean Theorem 2 of the square of the length of the longest side of a triangles is less than the sum of the squares of the lengths of the other two sides, then the triangles is an acute triangle
Converse of the Pythagorean Theorem 3 Of the square of the length of the longest side of a triangle is greater than the sum of the squares of the lengths of the other two sides, then the triangle the triangles is an obtuse triangle
Converse of the Pythagorean Theorem 3 of the altitude is drawn to the hypotenuse of a right triangle, the the two triangles formed are similar to the original triangle and and to each other.
Geometric Mean (Altitude) Is a right triangle, the altitude from the right angles to the hypotenuse divides the hypotenuse into two segments. the length of the altitude is the geometric mean of the lengths of the two segments
Geometric Mean (leg) In a right triangles, the altitude from the right angles to the hypotenuse divides the hypotenuse into two segments. the length of each leg of the right triangles is the geometric mean of the lengths of the hypotenuse and the segment of the hypotenuse tha
45-45-90 triangle In a 45-45-90 triangle, the hypotenuse is square root of 2
30-60-90 triangle in a 30-60-90 triangle, the hypotenuse is twice as long as the shorter leg, and the longer leg is the square root of 3 times as long as the shorter leg.
Created by: the cat